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Ex 6.1, 15 - The total cost C(x) = 0.007 x3 - 0.003 x2 - Ex 6.1

Ex 6.1,15 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.1,15 - Chapter 6 Class 12 Application of Derivatives - Part 3

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Ex 6.1, 15 The total cost C(𝑥) in Rupees associated with the production of 𝑥 units of an item is given by 𝐶(𝑥) = 0.007𝑥^3 – 0.003𝑥2 + 15𝑥 + 4000. Find the marginal cost when 17 units are produced.Since Marginal Cost is Rate of change in Total Cost w.r.t No of units produced Let MC be marginal cost So, MC = 𝒅𝑪/𝒅𝒙 Given, Total Cost = C(𝑥) =0.007𝑥^3−0.003𝑥^2+15𝑥+4000" " We need to find marginal Cost when 17 units are produced i.e. MC when 𝑥 = 17 MC = 𝑑(𝐶(𝑥))/𝑑𝑥 MC = 𝑑(0.007𝑥^3 − 0.003𝑥^2 + 15𝑥 + 4000)/𝑑𝑥 MC = 𝑑(0.007𝑥^3 )/𝑑𝑥 − 𝑑(0.003𝑥^2 )/𝑑𝑥+ 𝑑(15𝑥)/𝑑𝑥+ 𝑑(4000)/𝑑𝑥 MC = 0.007 𝑑(𝑥^3 )/𝑑𝑥 −0.003 𝑑(𝑥^2 )/𝑑𝑥 + 15𝑑(𝑥)/𝑑𝑥+0 MC = 0.007 × 3𝑥^2−0.003 ×2𝑥+15 MC = 0.021𝑥^2−0.006𝑥+15 We need to find MC when 𝑥=17 Putting 𝒙=𝟏𝟕 MC = 0.021(17)^2−0.006(17)+15 MC = 6.069 – 0.102 + 15 MC = 20.967 Hence, the Required Marginal cost is Rs. 20.967

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.